A computer can perform 30 identical tasks in six hours. At that rate,

Question

A computer can perform 30 identical tasks in six hours. At that rate, what is the minimum number of computers that should be assigned to complete 80 tasks within three hours?

A. 4
B. 5
C. 6
D. 7
E. 8

Archit3110 · Answer

a computer can do per hour 5 tasks and in 3 hours 15 tasks
so 80 tasks ; 80tasks can be done by 80/15: ~6 comptuers IMO C

stesmit · Answer

5 tasks per hour
So 5*3=15 tasks in 3 hours.

5*15=75 which isn't enough to complete 80 tasks
6*15=90 so you'll need 6 computers to complete the tasks in at least 3 hours.

C

abhishekdadarwal2009 · Answer

a computer can do per hour 5 tasks and in 3 hours 15 tasks

anything mire than 5, so 6 is the least

option C

fskilnik · Answer

Let´s use  UNITS CONTROL , one of the most powerful tools of our method!

? = {\left( {N\,\,{\mathop{m int}} } ight)_{\min }}\,\,\,{m{for}}\,\,\,\,\,{{80\,\,{m{tasks}}} \over {3\,\,{m{hours}}}}

1\,\,{m{comp}}\,{m{,}}\,\,{m{3h}}\,\,\, 	o \,\,\,15\,\,{m{tasks}}\,\,\,\,\,\left( {{{30\,\,{m{tasks}}} \over {6\,\,{m{hours}}}} = {{15\,\,{m{tasks}}} \over {3\,\,{m{hours}}}}} ight)

N\,\,{m{comp}}\,{m{,}}\,\,{m{3h}}\,\,\, 	o \,\,\,N \cdot 15\,\,{m{tasks}}\,\,\, \ge \,\,\,80\,\,{m{tasks}}

{m{N}}\,\, \ge \,\,{{80} \over {15}} = {{16} \over 3} = 5{1 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,? = 6

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

Archit3110 · Answer

Posted from my mobile device

fskilnik · Answer

Hi there!

There are always many similar ideas/solutions to any given problem.

If a different wording or a more structured presentation helps other members get a better comprehension, I guess the contribution is valid.

Regards,
Fabio.

Kimberly77 · Answer

Good explanation  fskilnik , result here is 5.333....why is minimum here not 5 but 6?
Could you help clarify? Thanks

fskilnik · Answer

Hello  Kimberly77  !

Sure! You need more than 5 computers... and six computers are enough... got it?

(The issue here is the fact that we look for the smallest integer that satisfies our needs!)

Regards and success in your studies,
Fabio.

Kimberly77 · Answer

ah totally make sense now, thanks a bunch fskilnik

A computer can perform 30 identical tasks in six hours. At that rate,

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